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Eigenvalue methods for time-dependent neuton diffusionOliveira, Roberto Gomes de, Instituto de Engenharia Nuclear 05 1900 (has links)
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Previous issue date: 1969-05 / The analysis of pulsed neutron experiments in multiplying and in nonmultiplying domains is considered. The analysis is based on the one-dimensional diffusion theory modelo In one-group models, a scalar version of problems similar to those of Sturm Liouville systems is generated; while in multigroup models, a vector version is required. An algorithm is suggested which allows the complete solution of the general scalar problem in all separable geometries of interest, for homogeneous boundary conditions. The results are the time igenvalues and the spatial eigen functions. The algorithm is suitable for direct computer implementation. Examples of application are given. The multigroup problem can be solved by adequate extensions of the one-group algorithm. Since the associated operators are nonselfadjoint, the eigenvalues form in general a spectrum that has a discrete plus a continuous part. All of the discrete spectrum can be obtained using the suggested method. An example with two groups of neutrons in a three-region domain is given. Extensions to inhomogeneous equations and boundary conditions are considered. Application of the methods to other problems rather than the pulsed neutron problem are studied. The method is shown to be useful in the solution of nonlinear boundary-value problems. Pulsed neutron experiments can be analyzed as problems similar to Sturm-Liouville systems. The scalar problems are completely solved here. The vector problems are partially solved. Some progress in the mathematical theory of nonselfadjoint operators is required for the complete solution of the vector problem.
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Etude de la methode de synthese iterative par deflation dans la resolution de l'equation de diffusion appliquee aux calculus des reacteursREIS FILHO, PAULO E.G. dos 09 October 2014 (has links)
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01262.pdf: 10916566 bytes, checksum: 2385abcdb07cf5e475019706bd6fea6f (MD5) / Tese (Doutoramento) / IPEN/T / Universite Scientifique et Medicale de Grenoble, France
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Etude de la methode de synthese iterative par deflation dans la resolution de l'equation de diffusion appliquee aux calculus des reacteursREIS FILHO, PAULO E.G. dos 09 October 2014 (has links)
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01262.pdf: 10916566 bytes, checksum: 2385abcdb07cf5e475019706bd6fea6f (MD5) / Tese (Doutoramento) / IPEN/T / Universite Scientifique et Medicale de Grenoble, France
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Application of a Constrained Optimization Technique to the Imaging of Heterogeneous Objects Using Diffusion TheorySternat, Matthew Ryan 2009 December 1900 (has links)
The problem of inferring or reconstructing the material properties (cross sections)
of a domain through noninvasive techniques, methods using only input and
output at the domain boundary, is attempted using the governing laws of neutron
diffusion theory as an optimization constraint. A standard Lagrangian was formed
consisting of the objective function and the constraints to satisfy, which was minimized
through optimization using a line search method. The chosen line search
method was Newton's method with the Armijo algorithm applied for step length control.
A Gaussian elimination procedure was applied to form the Schur complement
of the system, which resulted in greater computational efficiency.
In the one energy group and multi-group models, the limits of parameter reconstruction
with respect to maximum reconstruction depth, resolution, and number of
experiments were established. The maximum reconstruction depth for one-group absorption
cross section or multi-group removal cross section were only approximately
6-7 characteristic lengths deep. After this reconstruction depth limit, features in the
center of a domain begin to diminish independent of the number of experiments.
When a small domain was considered and size held constant, the maximum reconstruction resolution for one group absorption or multi-group removal cross section is approximately one fourth of a characteristic length. When finer resolution then this
is considered, there is simply not enough information to recover that many region's cross sections independent of number of experiments or flux to cross-section mesh refinement.
When reconstructing fission cross sections, the one group case is identical to absorption
so only the multi-group is considered, then the problem at hand becomes
more ill-posed. A corresponding change in fission cross section from a change in
boundary flux is much greater then change in removal cross section pushing convergence
criteria to its limits. Due to a more ill-posed problem, the maximum reconstruction
depth for multi-group fission cross sections is 5 characteristic lengths, which
is significantly shorter than the removal limit.
To better simulate actual detector readings, random signal noise and biased noise
were added to the synthetic measured solutions produced by the forward models.
The magnitude of this noise and biased noise is modified and a dependency of the
maximum magnitude of this noise versus the size of a domain was established. As
expected, the results showed that as a domain becomes larger its reconstruction ability
is lowered which worsens upon the addition of noise and biased noise.
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O Metodo da funcao de Green na solucao da equacao de difusao de neutrons para um reator cilindrico homogenio finito totalmente refletidoSANNAZZARO, LUIZ R. 09 October 2014 (has links)
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12885.pdf: 941021 bytes, checksum: 89af8f7af86b94c2e39f9dcd1cdcfa0b (MD5) / Dissertacao (Mestrado) / IEA/D / Escola Politecnica, Universidade de Sao Paulo - POLI/USP
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Utilizacao do metodo nodal absorcao-producao em calculos de distribuicoes de fluxo de neutrons e de potencia em uma dimensao e um grupo de energiaFERREIRA, CARLOS R. 09 October 2014 (has links)
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02573.pdf: 3007952 bytes, checksum: c5ad0aa94fbfe8573f958b6952ebfe9e (MD5) / Dissertacao (Mestrado) / IPEN/D / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP
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Utilizacao do metodo nodal absorcao-producao em calculos de distribuicoes de fluxo de neutrons e de potencia em uma dimensao e um grupo de energiaFERREIRA, CARLOS R. 09 October 2014 (has links)
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02573.pdf: 3007952 bytes, checksum: c5ad0aa94fbfe8573f958b6952ebfe9e (MD5) / Dissertacao (Mestrado) / IPEN/D / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP
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O Metodo da funcao de Green na solucao da equacao de difusao de neutrons para um reator cilindrico homogenio finito totalmente refletidoSANNAZZARO, LUIZ R. 09 October 2014 (has links)
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12885.pdf: 941021 bytes, checksum: 89af8f7af86b94c2e39f9dcd1cdcfa0b (MD5) / Dissertacao (Mestrado) / IEA/D / Escola Politecnica, Universidade de Sao Paulo - POLI/USP
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An algorithm for multi-group two-dimensional neutron diffusion kinetics in nuclear reactor coresSchramm, Marcelo January 2016 (has links)
O objetivo desta tese é introduzir uma nova metodologia para a cinética bidimensional multi- grupo de difusão de nêutrons em reatores nucleares. A metodologia apresentada usa uma aproximação polinomial em um domínio homogêneo retangular com condições de contornos não homogêneas. Como ela consiste em uma série de Taylor truncada, sua estimativa de erro varia de acordo com o tamanho do retângulo. Os coeficientes são obtidos principalmente pelas suas relações com o termo independente, que _e determinado pela equação diferencial. Estas relações são obtidas apenas pelas condições de contorno, e é demonstrado serem linearmente independentes. Um esquema numérico é feito para assegurar uma rápida convergência. Estes procedimentos feitos para um retângulo homogêneo são feitos para construir soluções para problemas de autovalor e dependentes do tempo de geometria ortogonal global com parâmetros seccionalmente constantes pelo método iterativo SOR. O autovalor dominante e sua autofunção são obtidos pelo método da potência no problema de autovalor. A solução para casos dependentes do tempo usam o método de Euler modificado na variável tempo. Quatro casos-teste clássicos são considerados para ilustração. / The objective of this thesis is to introduce a new methodology for two{dimensional multi{ group neutron diffusion kinetics in a reactor core. The presented methodology uses a polyno- mial approximation in a rectangular homogeneous domain with non{homogeneous boundary conditions. As it consists on a truncated Taylor series, its error estimates varies with the size of the rectangle. The coefficients are obtained mainly by their relations with the independent term, which is determined by the differential equation. These relations are obtained by the boundary conditions only, and these relations are proven linear independent. A numerical scheme is made to assure faster convergence. The procedures done for one homogeneous rectangle are used to construct the solution of global orthogonal geometry with step{wise constant parameters steady state and time dependent problems by the iterative SOR algo- rithm. The dominant eigenvalue and its eigenfunction are obtained by the power method in the eigenvalue problem. The solution for the time dependent cases uses the modi ed Euler method in the time variable. Four classic test cases are considered for illustration.
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Three dimensional heterogeneous finite element method for static multi‐group neutron diffusionAydogdu, Elif Can 01 August 2010 (has links)
Because current full‐core neutronic‐calculations use two‐group neutron diffusion and
rely on homogenizing fuel assemblies, reconstructing pin powers from such a calculation
is an elaborate and not very accurate process; one which becomes more difficult with
increased core heterogeneity. A three‐dimensional Heterogeneous Finite Element
Method (HFEM) is developed to address the limitations of current methods by offering
fine‐group energy representation and fuel‐pin‐level spatial detail at modest
computational cost. The calculational cost of the method is roughly equal to the
calculational cost of the Finite Differences Method (FDM) using one mesh box per fuel
assembly and a comparable number of energy groups. Pin‐level fluxes are directly
obtained from the method’s results without the need for reconstruction schemes. / UOIT
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